Cayley-Klein's model of dimension-free hyperbolic geometry via projective mappings

Link:

https://doi.org/10.1007/s00010-007-2899-1

Autor/in:

Benz, Walter

Erscheinungsjahr:

2008

Medientyp:

Text

Schlagworte:

Cayley-Klein model
Dimension-free
δ-affine
δ-linear
δ-projective

Beschreibung:

With respect to notation and notions we will follow our book Classical Geometries in Modern Contexts, Birkhäuser, 2005. If (X, δ), dim X ≥ 2, is a real inner product space, exactly the subsets H(a, α) = {x ε X | δ(a, x) = α} of X with 0 ≠ a ε X and α ε ℝ are called Euclidean hyperplanes of (X, δ). Concerning the notion of a quasi-hyperplane of (X, δ) see in our book, p. 50. In this note we characterize all δ-affine mappings of (X, δ), i.e. all bijections of X such that images and inverse images of Euclidean hyperplanes are Euclidean hyperplanes, by δ-linear mappings. As in our book we do not assume that X is finite-dimensional. Furthermore, we introduce δ-projective mappings and characterize Cayley-Klein's model dimension-free by those mappings. © 2008 Birkhäuser Verlag AG.

Lizenz:

info:eu-repo/semantics/closedAccess

Quellsystem:

Forschungsinformationssystem der UHH

Interne Metadaten

Quelldatensatz: oai:www.edit.fis.uni-hamburg.de:publications/5ad1aef9-9952-4c09-b2a8-9da948279624